Optimal factor group for nonsymmorphic space groups

Car, Roberto; Ciucci, G.; Quartapelle, L.

doi:10.1063/1.523016

Cited by 5 publications

(8 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Interestingly, we show that while our bulk monolayer is a symmorphic lattice, one particular cut leads the nonsymmorphic ribbon E, whose symmetry group is not a subgroup of its bulk counterpart. It is known that nonsymmorphism yields extra degenerescences with respect to its underlying point group [24][25][26][27][28] , which in our case results in an extra arXiv:1512.03249v2 [cond-mat.mes-hall] 12 Apr 2016 protection that preserves the Dirac cone for ribbons of arbitrary width. In addition to the fundamental physics presented here, the nonsymmorphic systems could be potential materials for nanoscale 2D devices, preserving the topological state properties even for nanosized ribbons.…”

Section: Introductionmentioning

confidence: 89%

“…Our main result is the unexpected nonsymmorphic space group D N S 2h of ribbon E, which yields extra topological protections 19,25 . Here the point group symmetry elements are the same as in D 2h , however, some of them must be complemented by a nonprimitive translation χ = a x of half a unit cell along x , i.e., glide planes and screw axis elements [24][25][26][27][28] . To obtain the matrix rep-resentation for these symmetry elements we use the same basis set from ribbon D above, but with the coordinates shifted (see Fig.…”

Section: B Ribbons D and Ementioning

confidence: 99%

“…Therefore we label the space groups with usual Schönflies notation of its corresponding point group. Ribbon E is a particularly interesting case, as it belongs to a nonsymmorphic space group [25][26][27] , and its symmetry operations are a combination of point group symmetries and translations by half a unit cell, i.e. glide planes and screw axes.…”

Section: Final Remarks and Conclusionmentioning

confidence: 99%

“…(A8). Reference 25,26 shows that for a nonsymmorphic crystal, one typically needs a factor group that is usually twice the size of the wave-vector group in order to close the multiplication table (not shown here). Indeed in our case we find that one needs the symmetry elements of Eqs.…”

Section: Nonsymmorphic Ribbon Ementioning

confidence: 99%

“…In this paper we build effective Hamiltonians using group theory [24][25][26][27][28] for a TCI monolayer and ribbons to investigate the effects of the edge terminations on its topological properties. A PbSe monolayer is chosen as a representative two-dimensional (2D) TCI for our discussion [29][30][31][32] .…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Topological nonsymmorphic ribbons out of symmorphic bulk

et al. 2016

View full text Add to dashboard Cite

States of matter with nontrivial topology have been classified by their bulk symmetry properties. However, by cutting the topological insulator into ribbons, the symmetry of the system is reduced. By constructing effective Hamiltonians containing the proper symmetry of the ribbon, we find that the nature of topological states is dependent on the reduced symmetry of the ribbon and the appropriate boundary conditions. We apply our model to the recently discovered two-dimensional topological crystalline insulators composed by IV-VI monolayers, where we verify that the edge terminations play a major role on the Dirac crossings. Particularly, we find that some bulk cuts lead to nonsymmorphic ribbons, even though the bulk material is symmorphic. The nonsymmorphism yields a new topological protection, where the Dirac cone is preserved for arbitrary ribbon width. The effective Hamiltonians are in good agreement with ab initio calculations.

show abstract

Section: Introductionmentioning

confidence: 89%

Section: B Ribbons D and Ementioning

confidence: 99%

Section: Final Remarks and Conclusionmentioning

confidence: 99%

Section: Nonsymmorphic Ribbon Ementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Topological nonsymmorphic ribbons out of symmorphic bulk

et al. 2016

View full text Add to dashboard Cite

show abstract

Electronic band structure of SnSe

Car¹,

Ciucci²,

Quartapelle³

1978

Physica Status Solidi (b)

Self Cite

View full text Add to dashboard Cite

R. CAR et al.: Electronic Band Structure of SnSe 471 phys. stat. sol. (b) 86, 471 (1978) Subject classification: 13.1 ; 22 htitWt0 d i Fi8ic.a del Politecnico (a) and Gmppo Nazionale d i 8tmttura dells Materia del C.N.R. (a), Milano Electronic Band Structure of SnSe BY R. CAR (a), G. CIUCCI (b), and L. QUARTAPELLE (a)The electronic bands of SnSe are calculated along all high symmetry lines of the Brillouin zone using the local empirical pseudopotential method. Spectralization of the involved large matrices is performed by means of a new approximate folding-down method which locates the s-states of valence bands much better than the Lowdin-Brust perturbative technique. The parameters of the analytical form used to interpolate the pseudopotentials are roughly adjusted to obtain a band structure consistent with optical and photoelectric data. Satisfactory results for the general features are obtained, a better agreement requiring a more cautious tuning of pseudopotential values in the region of small wave vectors.Die elektronischen SnSe-Biinder werden liings der Hochsymmetrie-Linien der Brillouin-Zone nach dem ortlichen empirischen Pseudopotentialverfahren berechnet. Die Eigenwerte der betreffenden groBen Matrizen werden mit einem neuen Niiherungsverfahren berechnet, wodurch die Energiewerte der s-Zustinde der Biinder vie1 besser als mit der Lowdin-Brust-Technik ermittelt werden. Die Parameter der Pseudopotentiale werden SO gewiihlt, daB eine zu den optischen und photoelektrischen Angaben passende Bandstruktur entsteht. Es werden befriedigende Ergebnisse in dem wesentlichen Verlauf erreicht, wobei fur eine bessere Ubereinstimmung eine vorsichtigere Einstellung der Pseudopotentialwerte im Gebiet der kleinen Wellenvektoren erforderlich ist.

show abstract

Induced projective representations

Dirl

1977

Journal of Mathematical Physics

View full text Add to dashboard Cite

The left- (right-) regular projective representation of a finite group G and the corresponding ’’projective’’ representation of the left-group algebra are defined for a given standard factor system, and special features of these constructions are discussed. Starting from a given projective unitary irreducible representation of a normal (but not necessarily Abelian) subgroup N of G, we obtain by induction the matrix elements of the projective unitary irreducible representations of G, where the corresponding group algebra is used as aid. These considerations are of interest for the construction of projective unitary irreducible representations of little cogroups of nonsymmorphic space groups. For the present method allows us to construct, for a q lying on the ’’surface’’ of the Brillouin zone, these projective representations out from unitary irreducible representations belonging to q’s of ’’lower’’ symmetry. This method is used to determine for all little cogroups of the nonsymmorphic space group Pn3n complete sets of projective unitary irreducible representations.

show abstract

Optimal factor group for nonsymmorphic space groups

Cited by 5 publications

References 17 publications

Topological nonsymmorphic ribbons out of symmorphic bulk

Topological nonsymmorphic ribbons out of symmorphic bulk

Electronic band structure of SnSe

Induced projective representations

Contact Info

Product

Resources

About